CHAPTER 01 · Read Cosmos
Eratosthenes and Earth’s circumference
Even if we cannot see the Earth in its entirety, can we still determine its size?
Explore this chapter ↗Let's begin! The experience allows you to directly interact with the scenes and observation tools.
Understand a vast world through a small observation
The book begins with more than the size of the universe. It asks how thought can reach beyond the senses. Eratosthenes brings that vast question down to a small shadow.
To connect the observations of two cities, assumptions are necessary. Under the assumption that the sunlight is nearly parallel and the Earth is spherical, the difference in angles between the two locations can be translated into the circumference of the entire planet.
OBSERVE · Start with evidence
Three pieces of evidence
- At the same time, a vertical object casts almost no shadow in one city but a clear shadow in the other.
- Both the distance between the two cities and the difference in solar altitude are measured together.
- 7.2° is 1/50 of 360°. Multiplying 800 km by 50 gives approximately 40,000 km.
From a shadow to the size of a planet
New commentary following the measurement story in chapter 1 of the original book. The values 800 km and 7.2° are approximations for exploring the principle, not a precise reconstruction of an ancient unit of distance.
When observations from afar and my own observations meet
It is difficult to determine the size of the Earth based solely on the length of shadows obtained in one city. It is necessary to connect what was observed from different locations at the same time. The information needed to understand the world is much broader than the perspective of a single person.
When connecting two observations, it is important to verify whether they were taken at the same time, whether the measuring stick was vertical, and what angle was measured. There is a quiet process of creating comparable measurements before making amazing calculations.
Questions to ConsiderThe records from the two cities are different. What should be compared first?
To scale a small circle to a full circle
If 7.2° represents 1/50th of the entire circle, then the length of the corresponding arc can be estimated as 50 times the circumference. In a rough model using 800 km between cities, this would be approximately 40,000 km.
This calculation assumes that the Earth is a sphere and that sunlight is nearly parallel. This simplification is not arbitrary; it is included to make the calculation easier. By adding conditions next to the numbers, others can review the reasoning.
Questions to ConsiderWhat would you include on a single line when presenting the results?
A method that outlasts an exact answer
If we only focus on how closely the measurements we have today match the measurements described in the text, we risk missing the true power of the story. Consider how the different observations at various locations are connected geometrically, even though we haven't physically walked the entire route.
Starlight and traces of the early universe raise a similar question: what evidence and models let us understand things we cannot touch? The small shadow in the first chapter is practice for reading the whole book.
Questions to ConsiderAnother observer has obtained different values than my conclusions. What should I do next?
Discoveries and their limits
Scientific reasoning is not a magic trick of extrapolating small data into large numbers. It involves revealing the assumptions made when connecting observations and reviewing the calculations.
Keep track of the values I obtained myself, the values I received from others, and the assumptions I made in my calculations.
Explore this chapter ↗Evidence and further reading
If we understand the size of a planet through physical laws, can we also explain the complexity of life as a natural process?